Spatially periodic solutions in a 1D model of phase transitions with order parameter

DOI10.1016/S0167-2789(98)00158-4zbMath0984.74058MaRDI QIDQ1964251

William A. Jester, Joseph Cusumano, Janusz Sikora

Publication date: 6 February 2000

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

wave equationstability analysisorder parameternucleationdiffusion coefficientnonlinear reaction-diffusion equationspatially periodic solutionsphase plane methodsannihilation of phase boundariesconvex strain energyisothermal stress-induced phase transitionsone-dimensional nonlinear bar

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Dynamics of phase boundaries in solids (74N20)

Cites Work

• Nonequilibrium thermodynamics of pseudoelasticity
• Structured phase transitions on a finite interval
• Co-existent phases in the one-dimensional static theory of elastic bars
• Equilibrium of bars
• Continuum theory of thermally induced phase transitions based on an order parameter
• On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models
• Dynamic solid-solid transitions with phase characterized by an order parameter
• Slow-motion manifolds, dormant instability, and singular perturbations
• Hysteresis and phase transitions
• Existence and uniqueness of global solutions to an extended model of the dynamical developments in shape memory alloys
• Thermo-mechanical evolution of shape memory alloys
• Stability of Singularly Perturbed Solutions to Systems of Reaction-Diffusion Equations
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)
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